Learn Finnish: Istummeko vierekkäin vai seläkkäin? - Do we sit next to each other or back to back?

It comes from the noun vieri (side). To add the mutual arrangement suffix, we use the stem viere- and add -kkäin. Literally, it means "side by side", which translates to "next to each other" in natural English.

Why does selkä (back) drop its 'k' to become seläkkäin?

This is due to consonant gradation. Adding the -kkäin suffix closes the syllable, which forces the word into its weak grade. The k in selkä disappears in the weak grade, giving us the stem selä-, to which we attach -kkäin.

Could I use tai instead of vai for the word "or" in this sentence?

No, you must use vai here. Vai is used in questions that offer specific, mutually exclusive choices (you are asking the listener to pick one). Tai is used in statements, or in open-ended questions where "both" or a simple "yes" could be a valid answer.

Let's break down istummeko. In what order do the suffixes attach to the verb?